Steady Stokes flow in a finite cylinder

This article addresses an analytical approach for solving the problem of steady three-dimensional creeping flow in a finite cylindrical container with arbitrary velocities prescribed over its surface. To illustrate the advantages of the developed approach, the flow in the container with a constant tangential velocity applied at one of the flat end walls is considered. It is shown that the local behaviour of the velocity field near the cylinder rim with discontinuity in velocities is similar to that of the Goodier-Taylor velocity field in a two-dimensional wedge. The kinematics of the corner eddy structures is illustrated by several numerical examples. It is shown that the structure of the corner eddies is more complicated compared with the well-known Moffatt corner eddies, the streamlines near the quiet rim of the cylinder having their spiral shapes.